Y. Wang, B. De Schutter, T.J.J. van den Boom, B. Ning, and T. Tang, "Real-time scheduling for trains in urban rail transit systems using nonlinear optimization," Proceedings of the 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), The Hague, The Netherlands, pp. 1334-1339, Oct. 2013.
The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of trains. Based on the passenger demand in urban rail transit systems, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. Three solution approaches are proposed to solve the real-time scheduling problem for trains: a pattern search method, a mixed integer nonlinear programming (MINLP) approach, and a mixed integer linear programming (MILP) approach. The performance of these three approaches is compared via a case study based on the data of the Beijing Yizhuang line. The results show that the pattern search method provides a good trade-off between the control performance and the computational efficiency.